Fire Resistance of Steel...

Fire Resistance of Steel Structures

Zdeněk SokolFrantišek Wald

České vysoké učení technické v Praze

2

List of lessons

1) Introduction to fire safety2) Fire load3) Advanced fire models 4) Structural analysis at fire, steel structures at fire5) Fire resistance of steel structures6) Fire resistance of composite structures7) Fire resistance of timber and aluminium

structures8) Fire resistance of concrete structures9) Fire resistance of timber and aluminium

structures 10) Loading at explosion11) Structural analysis at explosion 12) Robustness13) Fire tests

Design procedure

3

Introduction

Properties of steel at high

temperatures

Design models for structural

elements

Design models for joints

Conclusion

Thermal analysis

ČSN EN 1991-1-2

Temperature

ČSN EN 199x-1-2

Design model

ČSN EN 199x-1-2

of structural elementsof the fire compartment

EN 1991-1-2 EN 199x-1-2 EN 199x-1-2

Introduction

• Generally, the same method as for normal temperature is used

• The partial safety factor for steel at fire is

• The change of material properties caused by high temperature is very important

• Slightly different formulas are used when resistance to buckling (compression) or lateral-torsional buckling (bending) needs to be evaluated

• Attention should be paid to structural detailing, design of joints and maintaining the structural integrity to prevent the progressive collapse of the structure

4

0,1fi,M

Introduction


temperatures


elements


Conclusion

List of contents

• Properties of steel at high temperature

• The critical temperature method

• Classification of cross-sections

• Elements in tension

• Beams

• Elements in compression

• Beams subject to lateral-torsional instability

• Combination of bending and compression

• Elements with class 4 sections

• Connections

5

Introduction


temperatures


elements


Conclusion

Material testing at high temperature

6

External tenzometre

Thermal insulation

Furnace

Test specimen

Thermocouple

Heating device

Grip

Grip

Introduction


temperatures


elements


Conclusion

Properties of steel at high temperature

7

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0100 200 300 400 500 600 700 800 900 1000 1100 12000

Reduction factor

for yield limitky,

for proportional limitka,

for modulus of elaticitykE,

Temperature, °C

Introduction


temperatures


elements


Conclusion

Stress-strain diagram at high temperature

8Poměrné protažení

Napětí

E = tan a,

y, p, u,

f y,

f p,

t,

Introduction


temperatures


elements


Conclusion

Fire resistant steel

• Fire proof steel

– For industrial structures (furnaces, etc.) exposed to 600 °C to 1200 °C

• Fire resistant steel

– Fine crystal structure(reduced sulfur content)

– Addition of molybdenum andniobium

Used at EXPO 2000 in Hannover -The Christ Pavilion

9

Introduction


temperatures


elements


Conclusion

Fire resistant steel FRS275N

Increased yield limit at temperature 600˚C

10

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0100 200 300 400 500 600 700 800 900 1000 1100 12000

standard steelky,

standard steelkE,

Temperature, °C

steel FRS275Nky,

steel FRS275NkE,

Introduction


temperatures


elements


Conclusion

Critical temperature

11

8006004002000

Stress, MPaResistance of element

Load at fire situation


Temperature, °C700500300100 8006004002000

Utilization factor,


Temperature, °C700500300100

μ0

Surplus resistance

Collapse

1,0

0,8

0,6

0,4

0,2

0,0

Introduction


temperatures


elements


Conclusion


• Attention!

• The formula is applicable only to elements whose resistance depends on the yield limit only (no stability effects)

12

Utilization factor μ0

482196740

11939 8333

,

0cr,a

μ,ln,θ

fi,d,0

fi,d0 R

Eμ

Load at fire

Resistance at fire at temperature 20˚C

Introduction


temperatures


elements


Conclusion

Classification at normal temperature

… at normal temperature

where

13

yf235

Element Class 1 Class 2 Class 3

Flange c/tf=10

Web in bending

Web in compression

c/tf=11 c/tf=15

d/tw=72

d/tw=33

d/tw=83

d/tw=38

d/tw=124

d/tw=42

Introduction


temperatures


elements


Conclusion

Classification

The slenderness

The general formula

after simplification

14

kt4,28b

p

k123512E

tb

2

2p

k

fE904,0

tb

kfE

112

tb

kf

235123512E

tb

yy2

2

y2

2p

t

c

d

rw

tf

both values depend on the temperature

Introduction


temperatures


elements


Conclusion

Classification

The factor ε is used at normal temperature

It needs to be modified at high temperature

Simplified approach is used in standards

15

yf235

yf23585,0

y,y

,E

y,y

,E

,y fE

kk

fkEk

fE

Introduction


temperatures


elements


Conclusion

Classification at high temperature

… at high temperature

reduced ε

16

Element Class 1 Class 2 Class 3

Flange c/tf=10

Web in bending

Web in compression

c/tf=11 c/tf=15

d/tw=72

d/tw=33

d/tw=83

d/tw=38

d/tw=124

d/tw=42

yf23585,0

Introduction


temperatures


elements


Conclusion

Elements in tension

Elements with uniform temperature distribution in the cross-section

Non-uniform temperature distribution

17

fi,M

y,yRd,t,fi

fkAN

fi,M

n

iyi,,yi

Rd,t,fi

fkAN

1

Introduction


temperatures


elements


Conclusion

Laterally restrained beams, Class 1 and 2

Uniform temperature distribution (constant temperature)

Non-uniform temperature distribution (general method)

– neutral axis

– bending moment resistance

18

fi,M

y,yy,plRd,t,fi

fkWM

NN

fi,M

n

iyii,,yi

Rd,t,fi

fzkAM

1

temperature stress

Introduction


temperatures


elements


Conclusion

Laterally restrained beams, Class 1 and 2

Non-uniform temperature distribution (alternative method)

Adaptation factors– Factor κ1 to take into account non-uniform temperature of

the cross-section• κ1 = 1,00 for beams exposed on four sides

• κ1 = 0,70 for beams exposed on three sides with concrete slab on the fourth side

– Factor κ2 to take into account non-uniform temperature of the beam

• κ2 = 0,85 for intermediate supports of statically indetermined beams

• κ2 = 1,00 in other cases19

fi,M

y,yy,pl

21Rd,t,fi

fkWκκ

M

1

= 0,701

= 0,852

= 1,002

Introduction


temperatures


elements


Conclusion

Laterally restrained beams, Class 3

Uniform temperature distribution (constant temperature)

Non-uniform temperature distribution

the maximum temperature of the cross-section should be used for evaluation of moment resistance

20

fi,M

y,yy,elRd,t,fi

fkWM

fi,M

ymax,,yy,pl

21Rd,t,fi

fkWκκ

M

1

Introduction


temperatures


elements


Conclusion

Beams (shear resistance)

All sections

21

fi,M

yz,Vweb,,yRd,t,fi

fAkV

3

Introduction


temperatures


elements


Conclusion

Buckling resistance

For sections of class 1, 2 and 3– the maximum temperature should be used for non-uniform

temperature

– only one buckling curve with the imperfection factor α

Slenderness

Buckling reduction factor

where

22

fi,M

ymax,,yfiRd,t,fi,b

fkAN

yf, 235650

21 2

22

1

fi

,E

,y

kk

Introduction


temperatures


elements


Conclusion

Buckling reduction factors

23

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,0 0,4 1,0 1,4 2,0

0,2 0,6 0,8 1,2 1,6 1,8

0,21 - curve a0,34 - curve b0,49 - curve c0,76 - curve dfire - 500°Cfire - 700°C

0,13 - curve a 0

Introduction


temperatures


elements


Conclusion

Buckling resistance of element

24

0 50 100 150 2000

500

1000

1500

2500

2000

100×100×3,5steel S235

Slenderness

Resistance , kNNb,fi,t,Rd

25 75 125 175

20°C

300°C400°C

500°C

600°C

700°C800°C

Introduction


temperatures


elements


Conclusion

Reduction of buckling length of columns

• Generally, the buckling lengths at fire are the same as those at normal temperature

• The buckling lengths for multi-storey buildings can be reduced, when– it is non-sway structure

– there are separate fire compartments in each storey

– the floors have the same or higher fire resistance than the columns

25

0,7 L

0,5 L

0,7 L

Introduction


temperatures


elements


Conclusion

Unrestrained beams

• Beams with class 1 and class 2 sections– reduction of the yield limit is based on the temperature of

the compressed flange– the maximum temperature can be also used (conservative

approach)

• Beams with class 3 sections

Slenderness

Buckling reduction factor where

26

fi,M

ycom,,yy,plfi,LTRd,t,fi,b

fkWM

fi,M

ycom,,yy,elfi,LTRd,t,fi,b

fkWM

21 2

,LT,LT

,LT

22

1

,LT,LT,LT

fi,LT

,E

,yLT,LT k

k

yf, 235650

Imperfection factor

Introduction


temperatures


elements


Conclusion

Buckling reduction factor (lateral torsional instability)

27

LT,

LT,

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,0 0,4 1,0 1,4 2,0

0,2 0,6 0,8 1,2 1,6 1,8

0,21 - curve a 0,34 - curve b0,49 - curve c0,76 - curve d

fire - 500°Cfire - 700°C

hot-rolled H sections

hot-rolled I sections

welded H sections

welded I sections

Introduction


temperatures


elements


Conclusion

Bending and compression

• For class 1 and class 2 sections

– restrained elements (no lateral torsional instability)

– unrestrained elements (with lateral torsional instability)

• For class 3 sections

– similarly, but elastic section modulus is used

28

1

fi,M

y,yz,pl

Ed,zz

fi,M

y,yy,plfi,LT

Ed,yLT

fi,M

y,yfi,z

EdfkW

MkfkW

MkfkA

N

1

fi,M

y,yz,pl

Ed,zz

fi,M

y,yy,pl

Ed,yy

fi,M

y,yfimin,

EdfkW

MkfkW

MkfkA

N

Introduction


temperatures


elements


Conclusion

Class 4 sections

29

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,90

200

100

300

400

500

600

700

800Critical temperature ,°C

μ0

Utilisation factor,

a,cr

Elements with class1, 2 and 3 sections

Thin walled elements in tension

Beams with class 4 sectionsColumns with class 4 sections

1,0

Introduction


temperatures


elements


Conclusion

Class 4 sections

• As an alternative method, the resistance of thin-walled elements can be evaluated the same way as for class 3 sections, but effective section properties should be used

• The effective section properties can be evaluated at normal temperature

• The reduction factor for thin-walled sections (both, hot-rolled and cold-formed) is different from the factor for hot-rolled sections

30

Introduction


temperatures


elements


Conclusion

Reduction factors for thin-walled sections

• The reduction factors are used for thin-walled sections – cold-formed– hot-rolled, welded

31

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0100 200 300 400 500 600 700 800 900 1000 1100 12000

Reduction factor

for yield limit of hot-rolled sectionsky,

for yield limitky,

for modulus of elasticitykE,

Temperature, °C

of thin-walled sections

Introduction


temperatures


elements


Conclusion

Joints

• The joints are usually not the critical part of the structure, as the temperature is lower than the temperature of the connected elements

• There are requirements for structural integrity

To check resistance of the joints:• The temperature is the most important• The methods:

– simplified models for temperature– calculation using step by step method

with A/V ratio for the joint• The resistance calculation

can be based on component method adopted for high temperatures

32

Introduction


temperatures


elements


Conclusion

Temperature of the joints

Pictures from thermo cameras used to measure the beam to beam and beam to column connectionsa) Heating phase (30 min) b) The maximum temperature (54 min)

c) Cooling phase (69 min) d) The end (240 min)

33

31,5°C

945,9°C

200

400

600

800

SP01SP02SP03

430,0°C

750,0°C

500

600

700

SP01

SP02SP03

25,0°C

250,0°C

50

100

150

200

250

SP01SP02SP03

20,0°C

635,0°C

200

400

600

SP01SP02SP03

Introduction


temperatures


elements


Conclusion

Simplified model for temperature

Temperature of the beam supporting the concrete slab is based on beam temperature in the mid spanh < 400 mm

h > 400 mm

34

hh

,, k0h 301880

2pro21201880

2pro880

hhhh

,,

hh,

kk

0h

k0h

Concrete slab

h

400 mm0,62

0,75

0,88

> 400 mm

0,70

0,88

0,88

hk

0

0

0

h h0

0

0

Introduction


temperatures


elements


Conclusion

Temperature of the joint

Temperature of the joint depends on the location of the elements (bolts, weld, etc.)

35

hhk

720°C664°C

425°CIPE 360460°C

300

Introduction


temperatures


elements


Conclusion

Temperature by step by step method

Splice connection of the lower chord of the truss, R45 required

Unprotected connection

the fire resistance is 44 min 45 sec (standard curve)

Protected connection (protection thickness 15 mm)

the fire resistance is 112 min (standard curve)

36

4 × M24

P 28

85 125 40 45

150500 kN 500 kN

1m1843241

054 ,,

,VAm

13KWm288015010

241054

,,

,,

dVA

p

pp

Introduction


temperatures


elements


Conclusion

Reduction factors

EN 1993-1-2 gives the reduction factors for• bolts• welds

37

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0100 200 300 400 500 600 700 800 900 1000 1100 12000

Reduction factor

for yield limitky,

for weldskw,

for boltskb,

Temperature, °C

Introduction


temperatures


elements


Conclusion

Component method

Components– Resistance

– Stiffness

– Deformation

Joint– Resistance

– Stiffness

38

i,y,i FkF

i,E,i kkk

i,E

,y

,i

,i,i k

kkF

Rd,j,yRd,,j MkM

i ,i

,ini,j

k

zES

1

2

, mrad

M, kNm 20 ºC

800ºC

500ºC100ºC

50

0200 10040 60 80

600ºC

700ºC

M z

6070

203040

10

Introduction


temperatures


elements


Conclusion

Structural integrity

Axial force in the joint for various fire scenarios

39

Heating Cooling 720°C

I. Part of the beam (localised fire)II. Single beamIII. The whole floor

Axial force, kN

Time, min

The frame 60 80

300

200

100

0

-100

-200

- 300

20

100

40

4 × 6,0 m

The analysed joint 6 × 3,75 m

I. II. III.

Introduction


temperatures


elements


Conclusion

Comparison of different joints

40

Heating Cooling

Axial force, kN

100

-120-100-80-60-40-20

020406080

0

10 20 30 40 50 60 70 80 90Time, min

Introduction


temperatures


elements


Conclusion

Conclusion

41

• Simple design models for steel structures• Based on design at ambient temperature• Knowledge of material behaviour at high

temperature is necessary

• Joints usually do not represent critical part of the structure, no specialised check is necessary

• Simple temperature model for joints is available

• Proper detailing of joints ensuring structural integrity is very important

Introduction


temperatures


elements


Conclusion

Thank you for your attention

Zdeněk SokolFrantišek Wald

České vysoké učení technické v Praze

URL: www.ocel-drevo.fsv.cvut.cz

Fire Resistance of Steel...

Documents

Transcript of Fire Resistance of Steel...